Represent the given irrational numbers 3.5,9.4,10.5 on the real number line, and choose which number comes middle of the line.

(i) The first number we have = 3.5Now we can write that,=3.5+122-3.5-122=4.522-2.522=(2.25)2-(1.5)2Now, to draw given number of number lien make a line BC with measure 1.25 cmFrom point C, make a ray CX with the angle measure of 90∘From point B as center and 2.25 cm radius, make an arc that intersects CX at the point A. Join A to C.Length of this AC using Pythagoras theorem,AC=AB2-BC2=(2.25)2-(1.25)2=5.0625-1.5625=3.5 (ii) Number given in second part = 9.4Here,=9.4+122-9.4-122=10.422-8.422=(5.2)2-(4.2)2Make BC = 4.2 cm. From point C, make ray CX with angle measure of 90∘From B as centre with 5.2 cm radius make an arc that intersects CX at point A. Join A to C. Length of AC,AC= =AB2-BC2=(5.2)2-(4.2)2=27.04-17.64=9.4 (iii) Here, we have, 10.5Now,=10.5+122-10.5-122=11.522-9.522=(5.75)2-(4.75)2In the same way as perviours the line segment AC,AC=(5.75)2-(4.75)2=33.0625-22.5625=10.5000=10.5Option 2 is correct.

Represent the given irrational numbers 3.5,9.4,10.5 on the real number line, and choose which number comes middle of the line.

(i) The first number we have = 3.5Now we can write that,=3.5+122-3.5-122=4.522-2.522=(2.25)2-(1.5)2Now, to draw given number of number lien make a line BC with measure 1.25 cmFrom point C, make a ray CX with the angle measure of 90∘From point B as center and 2.25 cm radius, make an arc that intersects CX at the point A. Join A to C.Length of this AC using Pythagoras theorem,AC=AB2-BC2=(2.25)2-(1.25)2=5.0625-1.5625=3.5 (ii) Number given in second part = 9.4Here,=9.4+122-9.4-122=10.422-8.422=(5.2)2-(4.2)2Make BC = 4.2 cm. From point C, make ray CX with angle measure of 90∘From B as centre with 5.2 cm radius make an arc that intersects CX at point A. Join A to C. Length of AC,AC= =AB2-BC2=(5.2)2-(4.2)2=27.04-17.64=9.4 (iii) Here, we have, 10.5Now,=10.5+122-10.5-122=11.522-9.522=(5.75)2-(4.75)2In the same way as perviours the line segment AC,AC=(5.75)2-(4.75)2=33.0625-22.5625=10.5000=10.5Option 2 is correct.